6
votes
Accepted
If $0<\alpha<30^{0}$, then find value of $\log_{2}\left(\dfrac{8\cos(30^{0}-2\alpha)-\dfrac{8}{\cot(\alpha)+\cot(30^{0}-\alpha)}}{\sqrt3}\right)$
I believe the following method is quite short
\begin{align*}
\cot(\alpha) + \cot(30^{\circ} - \alpha) & = \frac{\cos(\alpha)\sin(30^{\circ} - \alpha) + \cos(30^{\circ}-\alpha)\sin(\alpha)}{\sin(\...
- 898
4
votes
Where am I wrong?
As noticed in the comments you have made a mistake at the third step, note also that when we take logarithm we need to satisfy some condition.
Notably, we can proceed as follows
$$5^x ≥ \frac{225+50x-...
- 160k
2
votes
Where am I wrong?
Too long for a comment.
As @user wrote, to finish the problem, you need to solve for $x$ the transcendental equation
$$5^x = \frac{10x+25}{x-2}$$ which happens to have an explicit solution in terms ...
- 274k
1
vote
Accepted
How to choose x positive integer such that x*2024^n has uneven number of digits for the longest time?
When you multiply by $2024$ you add either three or four digits to the number. You add three if there is no carry in the highest place, so you want carries as many times in a row as possible. This ...
- 380k
1
vote
If $0<\alpha<30^{0}$, then find value of $\log_{2}\left(\dfrac{8\cos(30^{0}-2\alpha)-\dfrac{8}{\cot(\alpha)+\cot(30^{0}-\alpha)}}{\sqrt3}\right)$
I calculated and got the value as 2.
Please recheck your answer.
Thank you.
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